Re: st: Relative Importance of predictors in regression

[Marcello Pagano <pagano@hsph.harvard.edu>]

I think we have belabored this point sufficiently.
I suspect that further discussion will not elicit any more light.
Thanks to all who partook in the discussion.
Let us agree to disagree.

m.p.


On 11/6/2013 2:52 PM, Lucas wrote:
> On Rich's point, of course if we estimate:
>
> 0. y=b1*YrsSchl + b2*Male
> 1. y=g1*YrsSchl + g2*Male + g3*white
> 2. y=h1*YrsSchl + h2*Male + h3*white + h4*age
>
> we would not expect b1=g1=h1 necessarily.  This has nothing to do with
> whether we have "held constant" the variables that are in model 0 when
> we are interpreting b1.
>
> On William's point, yes, the data has men and women in the example,
> else no expected values could be obtained for Y3 and Y4 in the
> example. So, paraphrasing William, he says, "You have adjusted your
> estimates for gender." Given that claim, what is the correct
> interpretation of b1 in model 0 above?  Sounds like you'd say "b1 is
> the difference in Y associated with a one year difference in YrsSchl,
> once the association between Y and sex has been accounted for." So,
> basically, this phrasing reduces to "b1 tells us the association once
> we hold constant all the other variables in the model, i.e.,
> differences in those variables DO NOT EFFECT our estimate of b1."
> [Note: if we interacted sex and education this interpretation would be
> inappropriate]. This is what I people mean when they say "held
> constant."
>
> It is interesting that there are varying interpretations of David H.'s
> point, which suggests his point escapes some and perhaps many.  I
> wonder if the formula he mentioned would clarify everything.
>
> Sam
>
> On Wed, Nov 6, 2013 at 11:37 AM, Richard Goldstein
> <richgold@ix.netcom.com> wrote:
> > Hi Sam,
> >
> > a little more seriously, consider the following two models:
> >
> > 1. y=b0 + b1*age + b2*female + b3*white
> > 2. y=b0 + b1*age + b2*female
> >
> > so, there is no reason to expect that either b1 or b2 would be the same
> > in these two models -- that I think is (part of) David's point
> >
> > I don't understand the "hold constant" part and how it might apply here,
> > or, really elsewhere when talking about the "effect" of a
> > right-hand-side variable; but I don't think that is what you are talking
> > about; so, I think that at least part of this discussion has people
> > talking past each other. Further, I don't think that this discussion is
> > related to the subject line either.
> >
> > Rich
> >
> > On 11/6/13, 2:22 PM, Lucas wrote:
> > > Hi Rich,
> > >
> > > Depends on which of us you ask.  I'd say if you compare a male w/ 9
> > > YrsSchl and a male w/ 8YrsSchl you've held sex constant and b1 is the
> > > difference in Y associated with that one year difference in schooling.
> > >   I think David H. would say that you've held nothing constant.  Is
> > > that a correct interpretation of your claim, David H.?
> > >
> > > Sam
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